Time-series quantum reservoir computing with quantum measurements*

The impact of interaction with the environment and measurement is significant in most quantum technologies, but it becomes even more critical in platforms requiring continuous monitoring. A challenging example is (classical) time-series processing such as speech recognition and chaotic series prediction and the search for enhanced data processing capabilities is driving research into quantum approaches. A promising avenue for sequential data analysis is quantum machine learning, with computational models such as quantum neural networks and reservoir computing (RC). Classical RC displays appealing features such as easy training and energy efficiency, and has recently been proposed in quantum settings. Quantum RC is better suited to quantum state processing and promises enhanced capabilities exploiting the enlarged Hilbert space. However, real-time processing and the achievement of a quantum advantage with efficient use of resources are prominent challenges towards viable experimental realizations. Our goal is to establish how quantum measurements can be efficiently incorporated into a realistic protocol. We discuss the conditions for efficient time-series processing while maintaining the necessary processing memory and preserving the quantum advantage offered by large Hilbert spaces. Efficient quantum RC is demonstrated, considering a transverse-field Ising network as a reservoir, for memory and prediction tasks with two successful measurement protocols. One repeats part of the experiment after each projective measurement. An alternative one uses weak measurements operating online where information can be extracted accurately and without compromising the required memory, despite back-action effects. We also propose a photonic platform suitable for real-time quatum RC. This is based on optical pulses circulating in a closed loop and operating in the continuous variable regime. While ideal operation achieves maximum capacities, statistical noise is shown to undermine any quantum improvement. We propose a strategy to overcome this limitation and maintain QRC performance as the size of the system is scaled up. The role of quantum squeezing is also discussed.